Some recommendations on these discussions are for good books to buy/download, and some are for specific stories. One of them has a series of stories introducing each great old one. In one discussion, I recommended a whole series of books from Chaosium that covers pre- and post-Lovecraft stories about the different great old ones. So you have options depending on how deep you want to get.

Also, check out the H P Lovecraft Literary Podcast. The hosts go through Lovecraft works chronologically, and offer fun/interesting commentary. It's an entertaining option if you want to go through the canon, and since the stories are mostly short the homework for each episode is manageable.

I always suggest to people "The Colour Out of Space". Like all Lovecraft tales it is a first-person narrative as he investigates a mysterious occurrence and at the end everything is back to normal and only he knows the truth. The story is short and very entertaining. In my opinion, a true staple is "Shadows over Innsmouth" (which if you watch the movie "Dagon" you'll get the idea). I enjoy "Call of Chuthlu" but all the action happens via the main character reading letters and newspaper clippings. Reading CoC is a must if you want to start a RPG champaign. Lastly, check out YouTube- there's a 2011 B&W "Call of Chuthlu" movie and a serial called "ShadowBound" made just last year (both are phenomenal!).